Nonlinear Estimation Approach Research Articles

Adaptive polynomial Kalman filter for nonlinear state estimation in modified AR time series with fixed coefficients

AbstractThis article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

The Impact of Institutional Factors on Bilateral Migration: the Gravity Approach

We explore the impact of institutional factors on bilateral migration among the EU, CIS, and the US by applying the gravity model of migration. We employ instrumental variables methodology (IV-PPML, IV-GMM) and a non-linear estimation approach (NLS) to test our assumptions about the spurring effect of institutional indicators on migration. Empirical results demonstrate a significantly positive effect of economic development and legislative system on migration flows in the sample countries. However, we find that government regulation and political stability decrease migration. We also find that Russia attracts CIS migrants due to cultural and institutional reasons, while the EU and the US accommodate migration due to economic reasons. The crucial role of institutional development as a determinant of international migration is often overlooked in contemporary literature. We generate new insight into the contribution of control for corruption and law, governmental regulation, political stability and democracy, and ease of doing business to migration. Based on the results, we provide some policy implications.

A novel nonlinear spectrum estimation method and its application in on-line condition assessment of bearing-rotor system

In this paper, a novel approach for nonlinear spectrum estimation is proposed and combined with Support Vector Machine (SVM) classifier to assess the condition of bearing-rotor systems, including fault types and severity. The proposed approach involves extraction and reconstruction of target harmonics, dynamic process modeling of the reconstructed signal based on a data-driven method, and extraction of nonlinear spectrum features in the form of nonlinear output frequency response functions (NOFRFs). The focus is on the influence of model stability and accuracy evaluation on the robustness of NOFRFs. Then the robustness of the NOFRFs based on the proposed estimation approach is compared with the conventional estimation approach using simulation cases and experiments. SVM is used to classify the extracted nonlinear spectrum features. Finally, the classification accuracy of NOFRFs evaluated by the proposed approach is compared with time-domain and frequency-domain features. Neighborhood Component Analysis (NCA) is used to select sensitive features and improve classification accuracy. The proposed condition assessment strategy does not require the selection of sensitive features, ensuring the stability of assessment results, which is also a significant advantage of the proposed strategy.

Active Carbon from Date Stones for Phenol Oxidation in Trickle Bed Reactor, Experimental and Kinetic Study

The catalytic wet air oxidation (CWAO) of phenol has been studied in a trickle bed reactor
 using active carbon prepared from date stones as catalyst by ferric and zinc chloride activation (FAC and ZAC). The activated carbons were characterized by measuring their surface area and adsorption capacity besides conventional properties, and then checked for CWAO using a trickle bed reactor operating at different conditions (i.e. pH, gas flow rate, LHSV, temperature and oxygen partial pressure). The results showed that the active carbon (FAC and ZAC), without any active metal supported, gives the highest phenol conversion. The reaction network proposed accounts for all detected intermediate products of phenol oxidation that composed by several consecutive and parallel reactions. The parameters of the model estimated using experimental data obtained from a continuous trickle bed reactor at different temperatures (120-160 C) and oxygen partial pressures (8-12 bar). Simple power law as well as Langmuir-Hinshelwood (L-H) expressions accounting for the adsorption effects were checked in the modeling of the reaction network. A non-linear multi-parameter estimation approach was used to simultaneously evaluate the high number of model parameters. Approach by simple power law only succeeds in fitting phenol disappearance. Instead, when L-H expressions are incorporated for the intermediate reaction steps, the model accurately describes all the experimental concentration profiles, giving mean deviations below 10%.

How did gold prices respond to the COVID-19 pandemic?

ABSTRACT This paper investigates the asymmetric impact of COVID-19 on gold prices by making use of high frequency data and a recently developed nonlinear estimation approach. The analysis considers three main dimensions of COVID-19: daily new cases, recoveries and deaths. The findings reveal that decreases in COVID-19 new cases and increases in recoveries cause an upswing in gold prices. These evidences imply that the reduction in new COVID-19 cases or more recoveries from COVID-19 improves both investors’ and consumers’ psychological confidence. In other words, the investors and consumers become more optimistic about their future and tend to demand more gold. On the other hand, the increases (decreases) in policy uncertainty, oil prices, and world stock index performance elevate (reduce) gold prices. The study also establishes a positive nexus between equity market uncertainty and gold prices.

Nonlinear Estimation and Control of Bending Soft Pneumatic Actuators Using Feedback Linearization and UKF

In this article, we combine nonlinear estimation and control methods for precise bending angle control in soft pneumatic actuators driven by a pressure source and single low-cost <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> / <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> solenoid valve. First, a complete model for the soft actuator is derived, which includes both the motion and pressure dynamics. An unscented Kalman filter (UKF) is used to estimate the velocity state and filter noisy measurements from a pressure sensor and an embedded resistive flex sensor. Then, a feedback linearization approach is used with pole placement and linear quadratic regulator (LQR) controllers for bending angle control. To compensate for model uncertainties and improve reference tracking, integral action is incorporated to both controllers. The closed-loop performance of the nonlinear estimation and control approach is experimentally evaluated with a soft pneumatic network actuator. The simulation and experimental results show that the UKF provides accurate state estimation from noisy sensor measurements. The results demonstrate the effectiveness and robustness of the proposed observer-based nonlinear controllers for bending angle trajectory tracking.

Extended Kalman filter and Takagi-Sugeno fuzzy observer for a strip winding system

This paper proposes two nonlinear estimation approaches, namely based on Extended Kalman Filter (EKF) and a Takagi-Sugeno Fuzzy Observer with 32 rules (TSFO-32), for a Strip Winding System (SWS) characterized by variable reference input, variable moment of inertia with constant increasing tendency and variable parameters. The SWS is a complex and nonlinear mechatronic system viewed as a controlled process, which wraps a strip with constant linear velocity on a reel, and the variable radius modifies both the angular velocity and the moment of inertia. The motivation of using EKF is the zero stationary error at low speeds. The motivation of using TSFO-32 is that once the Takagi-Sugeno fuzzy models are obtained, various analysis and design tools initially developed for linear systems, which facilitate the observation and/or synthesis of the controller for complex nonlinear systems, can be adapted appropriately and used in these nonlinear systems. Therefore, these tools simplify the design as well-established approaches and algorithms are available. The fuzzy control system stability and observer design conditions are derived and expressed as linear matrix inequalities. The efficiency of TSFO-32 is discussed in this paper in terms of setting a certain convergence rate. The performance of the two nonlinear estimation approaches is validated by means of digital simulations conducted for three values of the moment of inertia.

Whole-Body Parametric Imaging of 18F-FDG PET Using uEXPLORER with Reduced Scanning Time.

Parametric imaging of the net influx rate (Ki ) in 18F-FDG PET has been shown to provide improved quantification and specificity for cancer detection compared with SUV imaging. Current methods of generating parametric images usually require a long dynamic scanning time. With the recently developed uEXPLORER scanner, a dramatic increase in sensitivity has reduced the noise in dynamic imaging, making it more robust to use a nonlinear estimation method and flexible protocols. In this work, we explored 2 new possible protocols besides the standard 60-min one for the possibility of reducing scanning time for Ki imaging. Methods: The gold standard protocol (protocol 1) was conventional dynamic scanning with a 60-min scanning time. The first proposed protocol (protocol 2) included 2 scanning periods: 0-4 min and 54-60 min after injection. The second proposed protocol (protocol 3) consisted of a single scanning period from 50 to 60 min after injection, with a second injection applied at 56 min. The 2 new protocols were simulated from the 60-min standard scans. A hybrid input function combining the population-based input function and the image-derived input function (IDIF) was used. The results were also compared with the IDIF acquired from protocol 1. A previously developed maximum-likelihood approach was used to estimate the Ki images. In total, 7 cancer patients imaged using the uEXPLORER scanner were enrolled in this study. Lesions were identified from the patient data, and the lesion Ki values were compared among the different protocols. Results: The acquired hybrid input function was comparable in shape to the IDIF for each patient. The average difference in area under the curve was about 3%, suggesting good quantitative accuracy. The visual difference between the Ki images generated using IDIF and those generated using the hybrid input function was also minimal. The acquired Ki images using different protocols were visually comparable. The average Ki difference in the lesions was 2.8% ± 2.1% for protocol 2 and 1% ± 2.2% for protocol 3. Conclusion: The results suggest that it is possible to acquire Ki images using the nonlinear estimation approach with a much-reduced scanning time. Between the 2 new protocols, the protocol with dual injection shows the greatest promise in terms of practicality.

Age, growth, maturity and extinction risk of an exploited and endangered skate, Atlantoraja castelnaui, from off Uruguay and northern Argentina.

The spotback skate Atlantoraja castelnaui (Arhynchobatidae) is a large and threatened skate species subjected to fishing pressure, endemic to the Southwest Atlantic that occurs from Rio de Janeiro, Brazil, to San Jorge Gulf, Argentina. The age, growth, age at maturity and the maximum intrinsic rate of population increase rmax of A. castelnaui were studied using 152 specimens collected from off Uruguay and north Argentina (35°-42° S), between June 2013 and February 2020. Vertebrae from 143 individuals were used for ageing (females: n= 83, size range 404-1300 mm total length, TL; males: n= 60, size range 400-1270 mm TL). Maximum ages determined for females and males were 30 and 28 years, respectively. To fit growth models, non-linear and Bayesian estimation approaches were considered. For the first approach, a set of four candidate growth (size-at-age) models were fitted: three-parameter von Bertalanffy, two-parameter von Bertalanffy with fixed L0 , Gompertz and Logistic. In the second approach, von Bertalanffy, Gompertz and Logistic were fitted. For non-linear estimation, model selection indicated that the entire set of candidate growth models were supported by the data. The von Bertalanffy was selected as the best model for Bayesian estimation. There were no differences in growth between sexes. For the sexes combined, the von Bertalanffy growth model by Bayesian method was considered the most adequate to describe the growth of A. castelnaui (growth mean parameters ± S.D.: L∞ = 1210.29 ± 40.68 mm; k=0.12 ± 0.01 years-1 ; L0 = 179.20 ± 11.62 mm). The age at maturity was estimated at 16.21 and 14.04 years for females and males, respectively. The maximum intrinsic rate of population increase rmax was estimated as 0.252 years-1 . Life-history traits and rmax provided in the present study suggest that this species has a relatively low productivity and may be vulnerable to an intense fishing pressure.

Nonlinear total least-squares variance component estimation for GM(1,1) model

The solution of the grey model (GM(1,1) model) generally involves equal-precision observations, and the (co)variance matrix is established from the prior information. However, the data are generally available with unequal-precision measurements in reality. To deal with the errors of all observations for GM(1,1) model with errors-in-variables (EIV) structure, we exploit the total least-squares (TLS) algorithm to estimate the parameters of GM(1,1) model in this paper. Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation, we further present a nonlinear total least-squares variance component estimation approach for GM(1,1) model, which resorts to the minimum norm quadratic unbiased estimation (MINQUE). The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.

Is there an asymmetric link between the shadow economy and the financial depth of emerging market economies?

This study investigates the relationship between the shadow economy and financial depth for a group of 17 selected emerging countries over the period of 1980–2018 in both the long-run and short-run. The main feature of this study is to distinguish the short-run effects of the shadow economy from its long-run impacts by using the bounds testing approach to cointegration and error-correction modeling. Using a linear model estimation approach (ARDL), our findings show that, in a majority of countries, the existence of the shadow economy has a significant adverse impact on financial depth, implying that with an uncertain financial environment, there will be less opportunity to have a developed financial sector for this group of emerging market economies. Using the non-linear model estimation approach (NARDL), to investigate this relationship, we provide robust statistical evidence that the effect of the shadow economy on the depth of financial market development is not symmetric. The results indicate that despite similarities as emerging market economies, the estimated results could be very much country-specific in terms of unique country characteristics.

A Hybrid Nonlinear Forecasting Strategy for Short-Term Wind Speed

The ability to predict wind speeds is very important for the security and stability of wind farms and power system operations. Wind speeds typically vary slowly over time, which makes them difficult to forecast. In this study, a hybrid nonlinear estimation approach combining Gaussian process (GP) and unscented Kalman filter (UKF) is proposed to predict dynamic changes of wind speed and improve forecasting accuracy. The proposed approach can provide both point and interval predictions for wind speed. Firstly, the GP method is established as the nonlinear transition function of a state space model, and the covariance obtained from the GP predictive model is used as the process noise. Secondly, UKF is used to solve the state space model and update the initial prediction of short-term wind speed. The proposed hybrid approach can adjust dynamically in conjunction with the distribution changes. In order to evaluate the performance of the proposed hybrid approach, the persistence model, GP model, autoregressive (AR) model, and AR integrated with Kalman filter (KF) model are used to predict the results for comparison. Taking two wind farms in China and the National Renewable Energy Laboratory (NREL) database as the experimental data, the results show that the proposed hybrid approach is suitable for wind speed predictions, and that it can increase forecasting accuracy.

Second-Order Fault Tolerant Extended Kalman Filter for Discrete Time Nonlinear Systems

As missing sensor data may severely degrade the overall system performance and stability, reliable state estimation is of great importance in modern data-intensive control, computing, and power systems applications. Aiming at providing a more robust and resilient state estimation technique, this paper presents a novel second-order fault-tolerant extended Kalman filter estimation framework for discrete-time stochastic nonlinear systems under sensor failures, bounded observer-gain perturbation, extraneous noise, and external disturbances condition. The failure mechanism of multiple sensors is assumed to be independent of each other with various malfunction rates. The proposed approach is a locally unbiased, minimum estimation error covariance based nonlinear observer designed for dynamic state estimation under these conditions. It has been successfully applied to a benchmark target-trajectory tracking application. Computer simulation studies have demonstrated that the proposed second-order fault-tolerant extended Kalman filter provides more accurate estimation results, in comparison with traditional first- and second-order extended Kalman filter. Experimental results have demonstrated that the proposed second-order fault-tolerant extended Kalman filter can serve as a powerful alternative to the existing nonlinear estimation approaches.

Particle Gaussian mixture filters-I

In this paper, we propose a particle based Gaussian mixture filtering approach for nonlinear estimation that is free of the particle depletion problem inherent to most particle filters. We employ an ensemble of possible state realizations for the propagation of state probability density. A Gaussian mixture model (GMM) of the propagated uncertainty is then recovered by clustering the ensemble. The posterior density is obtained subsequently through a Kalman measurement update of the mixture modes. We prove the convergence in probability of the resultant density to the true filter density assuming exponential forgetting of initial conditions. The performance of the proposed filtering approach is demonstrated through several test cases and is extensively compared to other nonlinear filters.

Accelerated PET kinetic maps estimation by analytic fitting method

In this work, we propose and test a new approach for non-linear kinetic parameters' estimation from dynamic PET data. A technique is discussed, to derive an analytical closed-form expression of the compartmental model used for kinetic parameters' evaluation, using an auxiliary parameter set, with the aim of reducing the computational burden and speeding up the fitting of these complex mathematical expressions to noisy TACs.Two alternative algorithms based on numeric calculations are considered and compared to the new proposal. We perform a simulation study aimed at (i) assessing agreement between the proposed method and other conventional ways of implementing compartmental model fitting, and (ii) quantifying the reduction in computational time required for convergence. It results in a speed-up factor of ∼120 when compared to a fully numeric version, or ∼38, with respect to a more conventional implementation, while converging to very similar values for the estimated model parameters.The proposed method is also tested on dynamic 3D PET clinical data of four control subjects. The results obtained supported those of the simulation study, and provided input and promising perspectives for the application of the proposed technique in clinical practice.

Do people adapt to climate change? Evidence from the industrialized countries

PurposeThis study aims to explore the link between mortality and climate change. The focus is in particular on individuals’ adaptation to temperature changes. The authors analyze the relationship between climatic change (measured by temperature rate) and mortality in 23 Organisation for Economic Co-operation and Development countries during 1970-2010.Design/methodology/approachThis study performs the adaptation regression model in the level form as a dynamic panel fixed effects model. The authors use a non-linear threshold estimation approach to examine the extreme temperature changes effect on the temperature–mortality relation. More specifically, the study explores whether the large increases/decreases in temperature rates affect mortality rates more than the modest changes.FindingsThis study indicates that the temperature–mortality relation is significant in early part of the sample period (before 1990) but insignificant during the second part (after 1990). After including controlling factors, as well as nation and year fixed effects, the authors provide evidence that people do adapt to the most of the temperature-related mortalities. Also, this study provides evidence of the non-linear relationship between national temperatures and mortality rates. It is observed that only after 5 per cent increase in the annual temperature, the relation between temperature and overall mortality is significant.Originality/valueMost studies cover only one specific country, hence making it difficult to generalize across countries. Therefore, the authors argue that the best estimation of the health effects of temperature change can be found by modeling the past relationships between temperature and mortality across countries for a relatively long period. To the authors’ knowledge, previous studies have not systemically tested the adaptation effect across countries.

Characterizing the information content of cloud thermodynamic phase retrievals from the notional PACE OCI shortwave reflectance measurements.

We rigorously quantify the probability of liquid or ice thermodynamic phase using only shortwave spectral channels specific to the National Aeronautics and Space Administration's Moderate Resolution Imaging Spectroradiometer, Visible Infrared Imaging Radiometer Suite, and the notional future Plankton, Aerosol, Cloud, ocean Ecosystem imager. The results show that two shortwave-infrared channels (2135 and 2250 nm) provide more information on cloud thermodynamic phase than either channel alone; in one case, the probability of ice phase retrieval increases from 65 to 82% by combining 2135 and 2250 nm channels. The analysis is performed with a nonlinear statistical estimation approach, the GEneralized Nonlinear Retrieval Analysis (GENRA). The GENRA technique has previously been used to quantify the retrieval of cloud optical properties from passive shortwave observations, for an assumed thermodynamic phase. Here we present the methodology needed to extend the utility of GENRA to a binary thermodynamic phase space (i.e., liquid or ice). We apply formal information content metrics to quantify our results; two of these (mutual and conditional information) have not previously been used in the field of cloud studies.

IMPROVED NONLINEAR NOISE ESTIMATION IN EEG SIGNAL BASED ON VOLTERRA FILTERS

Recognition and compensation of undesired nonlinearity is one of the important subjects in the field of digital signal processing. The Volterra model is widely used for nonlinearity identification in practical applications. The current tendency in the digital systems design is the identification and compensation of unwanted nonlinearities. In this paper, we employed a nonlinear noise estimation approach for electroencephalogram (EEG) signal based on a combination of linear predictive coding (LPC) and Volterra filter that is a new and good way to estimate noise in EEG signal. We initially used LPC filter to estimate the noise present in EEG signal (correlated and uncorrelated noise) plus the uncorrelated portion of the signal (the part of the signal that has no linear relation to its past samples). After that, we employed nonlinear Volterra model to estimate the existing noise in EEG signal (correlated and uncorrelated noise). We show that by employing the cascade of LPC and Volterra filter, we can considerably improve the signal-to-noise ratio (SNR) in EEG signal by the ratio of at least 1.94. Also, we compared the simulation results to the case where we used just Volterra filter. In comparison with just Volterra filter, we have a significant increase in the SNR.

State profile estimation in a biomass gasification tubular reactor

The problem of estimating gas and solid concentration, as well as temperature and flow spatial profiles evolutions of a bistable tubular biomass gasification reactor from temperature measurements is addressed. The problem is addressed with a staged model-based geometric nonlinear estimation approach with robust convergence criterion and systematic tuning over the set of admissible estimation structures. By structure it is meant the number of model stages, the number of sensors, and their locations. The approach is illustrated with a representative start-up example studied before with experiments and simulation, finding that: the state profile evolutions can be estimated with a 6-stage model and two temperature measurements at sensitive locations before and after the hotspot.

Visual identification of biological motion for underwater human–robot interaction

We present an algorithm for underwater robots to visually detect and track human motion. Our objective is to enable human–robot interaction by allowing a robot to follow behind a human moving in (up to) six degrees of freedom. In particular, we have developed a system to allow a robot to detect, track and follow a scuba diver by using frequency-domain detection of biological motion patterns. The motion of biological entities is characterized by combinations of periodic motions which are inherently distinctive. This is especially true of human swimmers. By using the frequency-space response of spatial signals over a number of video frames, we attempt to identify signatures pertaining to biological motion. This technique is applied to track scuba divers in underwater domains, typically with the robot swimming behind the diver. The algorithm is able to detect a range of motions, which includes motion directly away from or towards the camera. Once detected, the motion of the diver relative to the vehicle is then tracked using an Unscented Kalman Filter, an approach for non-linear estimation. The efficiency of our approach makes it attractive for real-time applications on-board our underwater vehicle, and in future applications we intend to track scuba divers in real-time with the robot. The paper presents an algorithmic overview of our approach, together with experimental evaluation based on underwater video footage.